An Image is a visual stimulus with intensity and/or color varying as a 2-dimensional function of spatial position (I=I(x,y)). An image is substantially a continuous function.
In order to allow recording, storage, transmission, and/or manipulation of an image, some kind of abstraction, or representation is needed. A given image may have a plurality of possible representations. A representation can be symbolic (i.e., I(x,y)=x2+y), numerical—a table of numbers representing intensity values, chemical—exposed emulsion on a photographic film, etc.
The act of transforming of an image into one of its representations is referred to as Recording or Acquisition of the Image. Examples: Taking a photograph on film, scanning an image into computer memory, etc. While an image representation can be obtained from an image by recording it, it can also be synthesized, or generated artificially.
Rendering is the act of transforming an image representation into a visible image. Examples: display of a digitally stored image representation on a computer monitor; development of a photographic film; etc. Because a representation is not necessarily unique, and a plurality of (visually similar) images may be identically represented, the rendered image is not necessarily identical to the recorded image, but an approximation thereof. It is also possible to render an image from a synthetic representation. Such rendering can be used to visualize substantially non-visual (non-optical) phenomena. For example, the digitized signal from the detector of a scanning electron microscope (SEM) can be interpreted as a representation of an image, and thus can be rendered.
While an image is substantially continuous, its representation is not necessarily continuous. In particular, a Digital Image is a representation for which the image area is divided into a finite number of small elements referred to as picture elements, or pixels, and a number (with finite precision) is associated with each pixel to represent its intensity.
It is often useful to talk about regions and edges in an image. A Region in an image is a contiguous collection of image positions, which collectively possess a certain (substantially visual) property. Examples of such properties are average intensity, average color, texture or pattern, etc. An Edge in an image is a (substantially contiguous) collection of image positions that corresponds to the border between two adjacent regions. Much of the relevant information content of an image is contained in its edges.
Images contain information. Some of the information contained in an image is more relevant and some is less relevant to the viewer. The more relevant information a user can extract from an image, the more useful the image. One obstacle for extracting relevant information is noise. Noise in an image consists of variations in image intensity (or other property) which do not carry information that is relevant to the viewer. Noise often makes it more difficult for the viewer to extract the relevant information from the image. An image may become contaminated with noise during acquisition, manipulation and/or rendering.
A distinction is made between Fuzzy and Distinct edges. An edge in an image is fuzzy if a substantial amount of pixels near the edge and in one region are closer in property value to that of the other region, and vice versa. An edge is distinct, or sharp if the amount of such pixels is not substantial. An edge may be fuzzy due to inaccurate acquisition, to added (superimposed) noise, to certain filtering (convolution, blurring), or to other manipulations. Edge information is more difficult to extract from fuzzy edges.
Although the human visual system can extract information from images that are noisy, have fuzzy edges, or are otherwise less than ideal, it is possible to help it by enhancing the image. Image Enhancement is a transformation of an image (usually by manipulation of its representation) in order to obtain a substantially similar image that allows better visibility of certain aspects or components of the original image, thus allowing better and/or easier extraction of information relevant to the viewer.
Example: If a priori knowledge about a noisy image states that the spatial frequency of the noise is higher than that of the relevant information, one may apply a low-pass spatial filter in order to improve the ratio between relevant information (signal) and noise (signal-to-noise ratio, or SNR).
Another example: a plurality of representations of the same image, each containing independent noise with certain characteristics, can be averaged pixel-wise to improve SNR.
An image with fuzzy edges may be enhanced to obtain a similar image in which the edges are more distinct. Methods of this kind of enhancement are the subject of this invention.
Prior art smoothing techniques are discussed at chapter 3 of “The image processing handbook” by John C. Russ, CRC press 1994.
Noise reduction methods, such as smoothing and averaging out on one hand, and prior art edge enhancement and image sharpening methods on the other hand, are often contradictory in the sense that applying one increases the need for the other. Prior art methods often do not provide sufficiently visible images in cases where an image is both noisy and includes fuzzy edges.
Scanning electron microscopes are known in the art. U.S. Pat. No. 5,659,172 of Wagner describes a method for reliable defect detection using multiple perspective scanning electron microscope images. Scanning electron microscope images are generated by irradiating an inspected object with an electron beam, collecting signals resulting from an interaction of the electron beam with a portion of the surface of the inspected object and processing the collected signals. A magnification can be achieved if the electron beam is utilized to generate an image of a portion of the object that is smaller than the cross section of electron beam. A disadvantage of such a magnification is that the electron beam also interacts with other portions of the inspected object, and as a result the collected signals include unnecessary information that cannot be filtered out. In many cases this unnecessary information causes the image to include fuzzy edges.
There is a need to provide systems and methods for image enhancement of images that include fuzzy edges.
There is a need to provide systems and methods for image enhancement of images that are generated by scanning electron microscope imaging methods.
There is a need to provide systems and methods for image enhancement of images that are generated by scanning electron microscope imaging methods involving magnifications and especially large magnifications of an image.